Problem Solving? and necessary solutions.. Part 2?

Question

1. The length of a rectangle is three times the width. If the width is increased by 1 meter and the length is diminished by 2 meter, the area will be 78 sq cm. Find the dimensions of the original rectangle.

2. Ephraim is half the age of his brother. Five years ago, Ephraim was one-third the age of his brother. How old is Ephraim now?

3. How much of a 5% alcohol solution and how much of a 13% alcohol solution should be mixed to come up with 6 liters of an 8% alcohol solution?

4. The sum of the angles of any triangle is 180o. What are the three angles of a triangle if the sum of the first two angles is equal to the third angle and the difference of the first two angles is two-thirds of the third angle?

5. A purse contains $5.90 in nickels, dimes and quarters. The numbers of nickels is twice as many as the dimes, and there are two more quarters than dimes. How many coins of each type are in the purse? (Nickel = 5 cents, dime = 10 cents, quarter = 25 cents)

Answer 1

You'll write two equations for every question and solve.  For example,

1. l = 3w

(w + 1)(l-2) = 78

plug in "l" for the second equation. Solve for 'w', then plug that in to find 'l'.

2. e = ephraim's age    b = brother's age

e = 0.5b

b - 5 = 1/3e

solve again.

and so on.